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CENTRES OF SYMMETRIC CELLULAR ALGEBRAS

Part of: Representation theory of groups Conditions on elements

Published online by Cambridge University Press:  14 September 2010

YANBO LI
YANBO LI*
Affiliation:
Department of Information and Computing Sciences, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, PR China School of Mathematics Sciences, Beijing Normal University, Beijing, 100875, PR China (email: [email protected])
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Abstract

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Let R be an integral domain and A a symmetric cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ,S,T∈M(λ)}. We construct an ideal L(A) of the centre of A and prove that L(A) contains the so-called Higman ideal. When R is a field, we prove that the dimension of L(A) is not less than the number of nonisomorphic simple A-modules.

Keywords

symmetric cellular algebrascentre

MSC classification

Secondary: 16U70: Center, normalizer (invariant elements) 20C08: Hecke algebras and their representations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 511 - 522
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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